The maximum achievable solar concentration of a single reflective primary parabolic mirror is limited by its physical aspect ratio. The maximum concentration of a single refractive Fresnel lens is also largely limited by its chromatic aberration. To resolve these shortcomings, a ring-array concentrator (RAC) analytical model with variable aspect ratio is proposed here. The concentrator was composed of seven concentric parabolic reflective rings and a small Fresnel lens at the centre. A novel ring height modifier parameter (h d ) was integrated into the design model, which was complemented with the width of the rings (d w ), allowing the modification of each individual ring height. Different seven ring models were provided. Concentrated solar flux and optical efficiency were investigated with ZEMAX ray-tracing software for each model. Over 18 W/mm 2 concentrated solar flux and 54% optical efficiency were numerically achieved for most of these models. Novel ring-array designs with low total ring surface areas and low aspect ratios were also discussed. The best RAC concentrator configuration was found at d w = 60 mm and h d = 27.5 mm, which showed the highest concentrated solar flux of 18.7 W/mm 2 , high optical efficiency of 54.75%, while maintaining a moderate total RAC surface area of 1.81 m 2 and low aspect ratio of 0.50. The solar angle interaction and the associated tracking error were also studied. The proposed RAC model may constitute a very useful tool for designing advanced RACs by considering the strong influence of h d and d w on the key design parameters like concentrated solar flux, optical efficiency, total RAC surface area and aspect ratio.